\newproblem{lay:4_4_24}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.4.24}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Show that the coordinate mapping is \textit{onto} $\mathbb{R}^n$. That is, given any $\mathbf{y}\in\mathbb{R}^n$, with entries $y_1, y_2, ..., y_n$, produce
	a $\mathbf{u}\in V$ such that $[\mathbf{u}]_B=y$.
}{
  % Solution
	Assume that the basis $B$ is formed by the vectors $\mathbf{b}_1$, $\mathbf{b}_2$, ..., $\mathbf{b}_n$. Then the coordinates of the vector
	\begin{center}
		$\mathbf{u}=y_1\mathbf{b}_1+y_2\mathbf{b}_2+...+y_n\mathbf{b}_n$
	\end{center}
	are $\mathbf{y}$.
}
\useproblem{lay:4_4_24}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
